Dual-mode cellular systems based on the EIA/TIA IS-54 standard offer the eventual prospect of carrying up to six digital calls in the same bandwidth as a single analog call [1]. During the transition from analog to digital service, however, the call carrying capacity of such systems will be limited by the presence of existing analog users. In this situation, it is reasonable to ask if there are call-handling strategies that could increase the total traffic carried by providing preferential treatment to digital users. We consider four such strategies for maximizing the total traffic carried by a dual-mode cellular system. For two of these strategies, including the baseline 'no-control' strategy, we develop closed-form solutions for carried traffic and other related service statistics. The closed-form solution for the no-control case is then extended to provide a tight upper bound on carried traffic for any control strategy. We also present a method for finding the optimal control strategy by applying linear programming (LP) techniques. The strategies are compared for various proportions of analog and digital users and offered traffic levels. The findings show that it is actually quite difficult to obtain gains using strategies that exploit the difference in spectral efficiency between analog and digital calls, even with formally optimal strategies. While this is an unexpected finding, we feel the conclusion has been well validated and is now understood and explained in the paper. Index Terms--Land mobile radio cellular system, linear programming, queuing analysis, traffic control (communication).